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EDIT: There were some great answers here, and I realize this is a kinda broad question, but I'm accepting Monty Wild answer as it provided me with the info I needed to push this forward. Now I have a place to start research. Thanks everyone!

Giving a character "superhuman" strength is quite common in sci-fi, fantasy or just about any other genre, but how much is actually that strength varies wildly.

What is the strength limit for a humanoid?

For this "humanoid" is defined as:

  • Two legs
  • Two arms
  • Height between 1.75 and 2.15 m
  • Body volume around that of a fit male.

I'm not talking about giving superhuman strength to a human, it doesn't even needs to be organic, could be a robot) before you start breaking the laws of physics or requiring fictional materials?

I'm talking about peak short term strength here. How much can you lift and throw, how hard can a punch be. Actions that last a 1, 2, 10 seconds at most.

Imagine you can use whatever materials for the bones, skin, muscles, you are effectively designing it (with current or near future materials). Where do you draw the line, and how could you compute it? I imagine it has to do with the fracture strength of the bones and muscles, and how much the muscles contract. Guessing graphene bones and vanadium dioxide muscle would be about the best currently.

Assume that all the organs or electronic required to power up and control it are roughly the size of a brain, so you have the chest cavity free for other stuff.

Also, as a follow-up, how does this change if you start to admit more sci-fi stuff like unbreakable materials and the like. Mostly interested on the first part though.

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    $\begingroup$ What kind of strength are you referring to? That's not a rhetorical question; there's a big difference between, say, being able to lift a weight briefly (on the order of seconds to maybe tens of seconds) vs holding a weight steady for a long time (minutes or more). Can you edit your question to include a description of a situation in which you are aiming to maximize someone's strength? While questions about individual characters as such are off topic here, knowing how you will use the information can absolutely help shape answers. $\endgroup$ – a CVn May 11 '17 at 19:29
  • $\begingroup$ @MichaelKjörling Good point. Edited the question $\endgroup$ – Santiago Pacheco May 11 '17 at 19:34
  • $\begingroup$ "human sized", like a gas engine + big piston which can lift many tons, or humanoid? (Probably humanoid, but want to verify.) And if humanoid, how far from the American/European male height of 5'10" (178cm) and 160 lb (72 kg)? Because short people can lift more than tall people. $\endgroup$ – RonJohn May 11 '17 at 20:07
  • $\begingroup$ @RonJohn Edited the question. Not mentioning weight cause it'll be dependent on the material used. A guy with titanium bones will be quite heavier than a regular human, or someone with kevlar bones. $\endgroup$ – Santiago Pacheco May 11 '17 at 20:15
  • $\begingroup$ By mentioning graphene bones and vanadium dioxide muscles, you seem to be drifting into android territory. $\endgroup$ – RonJohn May 11 '17 at 20:17
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Many factors need to be taken into consideration in order to increase the effective strength of a humanlike form in a realistic manner. One can always scale up just a few of these factors and say, "Wow, look at how strong this would be!", but when put into practise in a real-world situation, something would either fail or limit the naïvely-calculated maximum exertion. This is a problem of engineering, not simply physics and materials science, and trade-offs will always have to be made.

  1. Strength of the materials: Stronger materials can withstand more force before being damaged. Any mismatch between actuator and skeletal strength increases the likelihood of mechanical failure.

  2. Density of the materials: The lighter the materials, the less force will be required to move objects made from them.

  3. The maximum force that can be applied by the actuators per unit mass: The more force that can be applied per unit mass, the less will be needed to simply move the individual's limbs, and the more that can be applied to the environment.

  4. The internal friction of the actuators and joints. The higher, the less efficient - and slower - the humanoid will be.

  5. The maximum speed of the actuators. Additional speed can be achieved by chaining actuators in series, but increasing strength requires that they be placed in parallel.

  6. The lever ratio of the humanoid's joints: Higher strength means lower speed.

  7. The maximum allowable time for a joint to transition between fully flexed and fully extended: The humanoid might otherwise be immensely strong, yet unable to outpace a snail.

  8. The energy efficiency of the actuators. Less efficient actuators require more energy input - and generate more waste heat, limiting the maximum duration of maximum exertion, as well as limiting the maximum number of actuators for the available cooling capacity and thermal tolerance. Given that no mechanism is ever 100% efficient, by rights, if his muscles were just as efficient as ours, Superman ought to glow visibly from the waste heat when he applies his super strength, though perhaps that's where the heat for his eyes' heat rays comes from...

  9. The thermal tolerance of the humanoid: Raise a human's temperature more than a few degrees, and the efficiency and efficacy of all sorts of things is significantly reduced. The same applies to most physical systems outside a vacuum.

  10. The cooling capacity of the humanoid: Humans have amongst the best cooling capacity of any species on earth, allowing a sufficiently fit individual to literally run down members of most other terrestrial animal species solely on the basis that a human can maintain an optimum body temperature while running at a pace at which causes pretty much every other animal species' body temperature to increase. Keep this up long enough, and the prey's rising body temperature will eventually cause a physical collapse. Additionally, with insufficient internal heat redistribution capacity, local temperature differences could increase to the point where localised damage would occur.

  11. The humanoid's available energy and its maximum rate of delivery to the actuators: There's no point in having actuators that consume vast amounts of power if sufficient power cannot be supplied to them, or if sufficient power can be supplied, but not for a sufficient amount of time.

  12. Whether the humanoid's actuators require an input of energy only when changing position or if energy is required to maintain a given force - i.e. electric screw-jack vs a long-travel electromagnetic linear actuator; the former requires power only to change its position, while the latter requires (more) power to maintain a given position somewhere between fully extended and fully contracted, and less (or none) when at the limits of its travel: Animal muscles fall into the latter category, increasing the basal metabolic cost of things as simple as maintaining a static standing posture, but if a humanoid had actuators that fell into the former category, only actuators actively moving would consume power, though maintaining a standing posture can be a rather more active task than it might seem.

  13. The humanoid's optimum operating temperature: If this is too different from the environmental temperature, then energy must be expended to maintain - or achieve - it, or the humanoid will suffer from losses of efficiency or from mechanical failure if its internal cooling or heating capacity cannot keep up with the rate of heat transfer, which increases proportionally to the difference in temperature.

  14. The humanoid's skin's insulation factor. By reducing the speed at which heat is gained or lost, this can increase the efficiency of the humanoid at rest, but can hamper the task of dealing with waste heat.

  15. The environmental temperature: While the average temperature is important when optimising a real mechanical system, the range of variation is also important. The lower the range of variation, the easier it is to optimise a system to operate in those conditions. Being able to tolerate a wider variety of conditions can be useful in being able to survive, but also increases the cost of insulation and cooling, and systems that accept a narrower range of acceptable conditions have lower metabolic requirements than those that accommodate all possible conditions, though at the cost of an increased probability of exposure-related injury or death.

  16. The mass of any support equipment required to allow the humanoid to function independently for a reasonable amount of time. Unless this humanoid is like an evangelion with a cable to its power supply - which would have its own problems - it'll have to carry everything it needs around with it. If it needs a lot of energy, it better have a compact way of storing that energy.

Evangelion with cable

So, as can be seen, this is a very difficult problem. Sure, you may want a 'superman', but you have to answer all of these questions - and more - before you can even begin to enumerate his realistic capabilities.

However, let's assume that we need a 'superman' with roughly human capacities for duration of exertion and with equivalent environmental optimums. We would need higher-strength materials, more powerful, lighter and more efficient actuators, and probably better cooling capacity too. Given intelligent design rather than evolution, we could achieve results that could never evolve naturally. We are still limited by real-world chemistry and physics, though.

It is not realistic to give a period of maximum exertion of as little as 10 seconds unless in that time your humanoid can achieve everything that a human could achieve in perhaps as much as 5 minutes. If your humanoid was this fast, it would have to have traded off a lot of strength - both structural and the force it could apply to external objects - to achieve that speed.

For a superhero, a realistic duration of elevated exertion would be more like 5 to 10 minutes. As a martial artist, practising karate and hapkido, at my dojo, the examination for black belt includes engaging in ten continuous minutes of fighting. Since a superhero might be able to achieve his results a bit faster than a mere human, five minutes might be a reasonable compromise.

If we build our superhero with light, strong materials like carbon fiber (perhaps 20 times stronger than human bone), use super-strong manufactured muscles that are up to a hundred times stronger than a human muscle like these, and provide a LENR atomic power supply, then it is conceivable that a human-sized and shaped form could lift (in an event such as the clean and jerk in Olympic weightlifting) not 263kg (the current human world record), but something on the order of 10,000kg.

However, being able to lift large weights is not all there is to being a superhero. Being able to lift ten tons at the same speed as a human doesn't mean that you punch any harder unless the actuators are also faster - if your arm weighs as much as a human's and accelerate just as fast, then the impact force will be the same. However, such a superhero could simply pick up a 50kg hand barbell in each hand and still get his punches out just as fast. Given the physics formula $e= 1/2mv^2$, artificially increasing the mass of a perhaps 10kg arm by 50kg and still hitting at the same impact speed would increase the impact energy by a factor of six, changing a punch from something that might break a bone if carefully placed to something far more likely to break bones every time it landed, or fatally concuss a human with a single punch most of the time.

However, if our intelligently-designed superhero was to do this for any length of time, say in a five-minute bout of all-out combat, then he would be generating a great deal more waste heat than any human in the same situation, requiring far more cooling capacity than even a 'merely' evolved human body can muster. His breath might be like a hair-dryer and/or his skin might literally steam with the amount of waste heat that would have to be dealt with.

On the other hand, if we gave our artificial superhero strength not a great deal greater than a human's - perhaps twice as strong at most - but a much higher speed, then he might be delivering punches that land at not ~9 m/s (32 kph or 20 mph), but at ~63 m/s (227 kph or 140 mph). That's 7 times the speed, but, because $e=1/2mv^2$, means that the punches will deliver 49 times the energy. That's the difference between bruising and perhaps a broken bone from a human fighter to a punch from our superhero that could almost literally knock the other guy's head off.

In order to control a body this responsive, we'd need to give our superhero light-speed electrical signalling instead of the downright sluggish electrochemical system our own nerves employ. This would also mean that our artificial superhero could literally watch a human opponent throw a punch at him, then - before that punch hit - throw six punches in return, each one potentially fatal or crippling before finally blocking the incoming punch, assuming that energy transfer to his opponent didn't knock him so far back as to make blocking the initial punch entirely unnecessary.

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Hard Science Upper bound

How hard could you punch? Lets say you only need to be able to throw one punch and you want to hit as hard as possible.

Let's assume that you have to bring your power supply with you (you can't haul a generator with you)

Let's assume you have a perfect generator that converts mass to energy as effectively as possible.

Let's assume the you consume all of you available mass and energy in the one punch/explosion. A shock wave is like a punch, right?

The available kinetic energy would be $m \cdot c^2$; an 80 kg humanoid would hit with $7 \cdot 10^{18}$ Joules.

The Tsar bomb (most powerful nuclear bomb) was $4.2 \cdot 10^{16}$ Joules.

So, the most energy that a human mass could output is about 100 Tsar bombs. This would be true no matter what materials you use, your limited mass gives you a limited output.

At first this upperbound seems useless but it eliminates some fictional examples, such as humanoids destroying or moving planets. There just is not enough mass / energy in a humanoid unless they have an exterior source.

Edit: If the person can be much denser than their destructive power increases linearly with their mass.

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    $\begingroup$ "He punched so hard he disappeared!" $\endgroup$ – Isaac Kotlicky May 12 '17 at 2:24
  • $\begingroup$ weight would vary a bit due to length. "Height between 1.75 and 2.15 m", 80kg is okay for 1.75, maybe a little bit too much for a fit male, but it is certainly too skinny for a male of 2.15m. I would expect about 110kg for someone at 2.15m. Making the effect even better. $\endgroup$ – Mixxiphoid May 12 '17 at 6:38
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As per my link in the comments on Hysterical strength (https://en.wikipedia.org/wiki/Hysterical_strength) it is entirely likely that the current human form is actually significantly stronger than what we are capable on a day to day basis. Somewhere along human development, the brain started to stop and think as opposed to instinctively react and this seems to have impacted or strength heavily. Gorillas are estimated to have 6 to 15x the strength of humans pound for pound, displaying how exaggerated this actually is. I also think there is some degree of trade-off between precision vs strength, a trade off humanity made quite some time ago.

There is also the Berserk warrior legends, warriors renowned for foaming at the mouth while gnawing on their own iron shields, that could enter a frenzy (read as dropping thought for instinct) and perform feats of strength that were well beyond anything other humans could perform. Though these feats are not only hard for the body to perform, but also damaging as the muscle itself can tear itself, tendon, and bone apart (temporal brain can figure out damage to its body may have short term gain, but harsh future implications and therefore only allow access to this strength when short term damage is deemed worthy regardless of future considerations).

The greatest feat I can readily find comes from the hysterical strength link where 2 female children (age 14 and 16) managed to lift a tractor off of their father (around 15x what they'd normally lift). Most of the evidence on this is anecdotal, but its prevalent enough to give some credit to the theory.

For hard numbers, I'll use deadlift with the world record of 500kg (1100) lbs, though without equipment it's 460kg. The world record of 500kg was set by Eddie Hall, who nearly died from the attempt (http://www.independent.co.uk/sport/general/eddie-hall-nearly-died-after-passing-out-following-new-deadlift-world-record-of-500kg-a7132306.html) due to bursting blood vessels in his head from this attempt. There has also been several occurrences of dead lifters losing their bowels (not bowel content, the lower bowel literally gets ejected out the rear end). I'd actually consider this the maximum limit of the human form, not because of the upper limit of human muscle, but the upper limit of pressure our internal organs and brain can actually handle.

That being said, if Eddie Hall entered a frenzy or Hysterical strength, it is possible his upper limit could be between 6x-15x that of his regular strength...gives a value of 3000kg to 7500kg as a potential. Of course, big disclaimer saying that these muscles may be capable of handling it, but the forces exerted on the bodies organs and brain would likely be well beyond what we can tolerate resulting in a quick death. Interesting that our internal organs are ultimately the limiting factor here.

Added - I did suggest that a lot of hysterical strength is anecdotal. In the case of the 14 and 16 year old : http://www.dailymail.co.uk/news/article-2307079/Teen-sisters-lift-3-000lb-tractor-rescue-father-pinned-underneath.html
They managed to lift a 3000lbs tractor high enough for their father to wiggle free. There is much speculation that there was something else contributing (tractor was leaning a bit to one side and the children simply tilted it)...so it's hard to say what was done here, simply because 'hysterical strength' is exceedingly difficult to measure in a controlled setting.

There is some researchers whom have suggested we could measure the maximum strength of a person through electric shocks (basically using an electric current to over ride the muscle and force it to contract as hard as it possibly can). But I can only find the theory, I can't actually find anywhere that the experiment was actually tested.

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    $\begingroup$ Gorillas are stronger not just because of their higher muscle mass, but because of lever ratios. Imagine a pair of sticks with a hinge between them, and a spring extending from the top of the upper stick to a point near the hinge on the lower. The force that can be applied at the end of the lower stick is the force of the spring multiplied by the distance from the hinge to the spring divided by the distance from the spring to the end. The further from the hinge the spring attaches, the more force. However, speed inverts this relationship. Gorillas are stronger, but humans are faster. $\endgroup$ – Monty Wild May 12 '17 at 1:34
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    $\begingroup$ Also, the problem with electrical activation of muscles is that in order to get complete activation, you need high voltages - like 70-100V. This is painful and potentially injurious, and no ethics committee would approve such an experiment. Nerves do the job much better, but you'd have to do surgery to isolate and then stimulate the nerve, and again, given the risks inherent in any surgery, that wouldn't likely be approved. To do this ethically, you'd need a limb amputated from someone with body dysmorphic disorder, right after surgery. Not so easy... $\endgroup$ – Monty Wild May 12 '17 at 1:41
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    $\begingroup$ As for the tractor, it had toppled on its side and the man was pinned by the steering wheel. Given that tractors have large rubber rear wheels and have suspension springs, the balance of the mass on the ground would have ensured that the man wasn't being pinned by the whole mass of the tractor, but by a considerably lower effective mass, such that two teenage girls could apply a sufficient counterforce to allow him to escape. The fact that his arm was bruised and not broken attests to this. This is not theoretical physics with rigid cubical tractors. $\endgroup$ – Monty Wild May 12 '17 at 1:58
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    $\begingroup$ @MontyWild - Correct on the Gorrilla, though if you go silverbacks, they outrun us too. We're more agile mind you. And yes to the electrical experimental issues, likely why that field hasn't progressed...I'd imagine trying to put someone into a hysterical strength situation is likely as unethical. I've got some more research to append to my answer now, it appears we average around 2/3s of our strength on a day to day level and can go 50% beyond that during 'hysterical' times...far less than my answer tries to state. Body builders and intense training can push the number closer to 80 or 90% $\endgroup$ – Twelfth May 12 '17 at 15:58
  • $\begingroup$ When I said 'speed' I meant 'angular velocity of joint motion', not how fast the creature covers ground. Gorillas are quadrupeds, but if they can't use their arms, humans run much faster. More legs means more ground covered per gait cycle. $\endgroup$ – Monty Wild May 13 '17 at 7:27
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If you would like to strengthen a human, which its body mechanics, strongest parts of the human body are bones, and they have about 120MPa tensile strength.

enter image description here source

So if we would take something 1000 times stronger (carbon nanotubes), we probably could make a humanoid body 1000 times stronger than a typical fit human.

The tensile strength of muscles varies from 3kPa to 70kPa for different species and conditions (source). There is somewhere in internet human muscles strength, but because of paywalls and lack of patience, let's use higher number available. The number definitely shows that muscles could be improved significantly.

So if we shift proportion by making bones thicker, and muscles of the same 120GPa materials, we definitely can expect improvements more than 1000 times. For my opinion, 10000 times could be a good guess.

So if you would like to keep human like biomechanics 10'000 stronger is a good number, however, it is not the limit to humanlike shape.

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Hard Science Lower Bound

What could you make today?

As a lower bound what could you make with materials available today. Hydrolics are much stronger than muscles. So lets make a humanoid with a torso that is just a large hydraulic piston that telescopes up and down. The robot lifts with its torso From the wiki page we see industrial hydraulics can have 6000 psi systems, but 2,000 psi are more common. Wiki on hydraulics

The area of the piston would be the cross-sectional area of a humans waist/stomach. Lets assume a fat human so the cylinder will be circular a 40 inch waist is radius of 20 and area of 1,256 inches ^2

This gives a max lift strength of 3,768,000 7,536,000 pounds.

So given today's technology we could build a hydraulic piston shaped like a human that could lift 1,800 - 3,600 tons

This assumes that we uses the rest of the volume for the pump, fuel, and hydraulic fluid reserves, but it seems reasonable. We could do scaled down versions for the other limbs.

Fair warning a humanoid trying to lift that much weight would be apply around 2,000 psi to the ground underneath it which would break most floors and many roads.

Edit: Credit to RonJohn for mentioning this idea before I thought of it.

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  • $\begingroup$ do not flatter yourself those answers are science-based, not hs :) $\endgroup$ – MolbOrg May 12 '17 at 0:20
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You can be as strong as you want if you have the infrastructure to support it, so if you make the bones more robust you can up the strength to the limits of muscle power, which in other primates is a lot more than humans.

I think you could reasonably make your people 10 times stronger without breaking any laws with thicker bones or different composition of the bones making them stronger and gorilla type muscles.

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    $\begingroup$ I would argue that you are borderline not answering the question since you just reiterate the premise of the question and answer it with the number ten. Do you have any basis for it to be 10 times stronger, or is that just a "nice number" guess based on that other primates are stronger than us? $\endgroup$ – Mrkvička May 11 '17 at 20:03
  • $\begingroup$ @Mrkvička it's just a guess, since we don't have any data on tungsten bones and fibreglass muscles, I'm scaling up gorilla muscles with stronger bones. Gorillas don't weight train, humans that do greatly increase there strength so I'm using that assumption. $\endgroup$ – Kilisi May 11 '17 at 20:20

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